Divide. Write Your Answer In Simplest Form. 13 15 ÷ 7 10 \frac{13}{15} \div \frac{7}{10} 15 13 ​ ÷ 10 7 ​

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Introduction

In mathematics, division is a fundamental operation that allows us to find the quotient of two numbers. It is an essential concept in arithmetic and algebra, and it plays a crucial role in solving various mathematical problems. In this article, we will explore the concept of division, particularly the division of fractions, and learn how to divide fractions in the simplest form.

What is Division?

Division is the inverse operation of multiplication. It is a mathematical operation that involves finding the quotient of two numbers. The quotient is the result of dividing one number by another. For example, if we divide 12 by 3, the quotient is 4, because 3 multiplied by 4 equals 12.

Dividing Fractions

Fractions are a type of number that represents a part of a whole. They are written in the form of a/b, where a is the numerator and b is the denominator. When we divide fractions, we need to follow a specific set of rules to ensure that the result is in the simplest form.

The Rule for Dividing Fractions

To divide fractions, we need to follow the rule:

a/b ÷ c/d = (a × d) / (b × c)

where a, b, c, and d are numbers.

Applying the Rule to the Given Problem

Now, let's apply the rule to the given problem:

1315÷710\frac{13}{15} \div \frac{7}{10}

Using the rule, we can rewrite the problem as:

1315÷710=13×1015×7\frac{13}{15} \div \frac{7}{10} = \frac{13 \times 10}{15 \times 7}

Simplifying the Expression

To simplify the expression, we need to multiply the numerators and denominators:

13×1015×7=130105\frac{13 \times 10}{15 \times 7} = \frac{130}{105}

Reducing the Fraction to its Simplest Form

To reduce the fraction to its simplest form, we need to find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 130 and 105 is 5.

Dividing both the numerator and denominator by 5, we get:

130105=2621\frac{130}{105} = \frac{26}{21}

Conclusion

In conclusion, dividing fractions is a simple yet powerful operation in mathematics. By following the rule for dividing fractions, we can simplify complex expressions and find the quotient of two fractions. In this article, we learned how to divide fractions in the simplest form and applied the rule to a given problem.

Final Answer

The final answer to the problem 1315÷710\frac{13}{15} \div \frac{7}{10} is 2621\frac{26}{21}.

Additional Examples

To reinforce your understanding of dividing fractions, let's consider a few more examples:

  • 34÷56=3×64×5=1820=910\frac{3}{4} \div \frac{5}{6} = \frac{3 \times 6}{4 \times 5} = \frac{18}{20} = \frac{9}{10}
  • 23÷45=2×53×4=1012=56\frac{2}{3} \div \frac{4}{5} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12} = \frac{5}{6}
  • 58÷34=5×48×3=2024=56\frac{5}{8} \div \frac{3}{4} = \frac{5 \times 4}{8 \times 3} = \frac{20}{24} = \frac{5}{6}

Practice Problems

To practice dividing fractions, try the following problems:

  • 79÷23=?\frac{7}{9} \div \frac{2}{3} = ?
  • 45÷32=?\frac{4}{5} \div \frac{3}{2} = ?
  • 910÷65=?\frac{9}{10} \div \frac{6}{5} = ?

Answer Key

  • 79÷23=7×39×2=2118=76\frac{7}{9} \div \frac{2}{3} = \frac{7 \times 3}{9 \times 2} = \frac{21}{18} = \frac{7}{6}
  • 45÷32=4×25×3=815\frac{4}{5} \div \frac{3}{2} = \frac{4 \times 2}{5 \times 3} = \frac{8}{15}
  • 910÷65=9×510×6=4560=34\frac{9}{10} \div \frac{6}{5} = \frac{9 \times 5}{10 \times 6} = \frac{45}{60} = \frac{3}{4}
    Divide: A Simple yet Powerful Operation in Mathematics - Q&A ===========================================================

Introduction

In our previous article, we explored the concept of division, particularly the division of fractions, and learned how to divide fractions in the simplest form. In this article, we will answer some frequently asked questions about dividing fractions to reinforce your understanding of this concept.

Q&A

Q: What is the rule for dividing fractions?

A: The rule for dividing fractions is:

a/b ÷ c/d = (a × d) / (b × c)

where a, b, c, and d are numbers.

Q: How do I simplify a fraction after dividing?

A: To simplify a fraction after dividing, you need to find the greatest common divisor (GCD) of the numerator and denominator. Then, divide both the numerator and denominator by the GCD.

Q: What is the difference between dividing fractions and multiplying fractions?

A: Dividing fractions is the inverse operation of multiplying fractions. When you divide fractions, you are finding the quotient of two fractions, whereas when you multiply fractions, you are finding the product of two fractions.

Q: Can I divide a fraction by a whole number?

A: Yes, you can divide a fraction by a whole number. To do this, you need to multiply the fraction by the reciprocal of the whole number. For example, to divide 1/2 by 3, you need to multiply 1/2 by 1/3.

Q: How do I divide a fraction by a decimal?

A: To divide a fraction by a decimal, you need to convert the decimal to a fraction and then divide the fractions. For example, to divide 1/2 by 0.5, you need to convert 0.5 to a fraction, which is 1/2. Then, you can divide 1/2 by 1/2.

Q: Can I divide a negative fraction by a positive fraction?

A: Yes, you can divide a negative fraction by a positive fraction. When you divide a negative fraction by a positive fraction, the result will be a negative fraction.

Q: How do I divide a fraction by a fraction with a zero denominator?

A: You cannot divide a fraction by a fraction with a zero denominator. This is because division by zero is undefined.

Q: Can I divide a fraction by a fraction with a negative denominator?

A: Yes, you can divide a fraction by a fraction with a negative denominator. When you divide a fraction by a fraction with a negative denominator, the result will be a fraction with a negative denominator.

Practice Problems

To practice dividing fractions, try the following problems:

  • 79÷23=?\frac{7}{9} \div \frac{2}{3} = ?
  • 45÷32=?\frac{4}{5} \div \frac{3}{2} = ?
  • 910÷65=?\frac{9}{10} \div \frac{6}{5} = ?
  • 12÷3=?\frac{1}{2} \div 3 = ?
  • 12÷0.5=?\frac{1}{2} \div 0.5 = ?

Answer Key

  • 79÷23=7×39×2=2118=76\frac{7}{9} \div \frac{2}{3} = \frac{7 \times 3}{9 \times 2} = \frac{21}{18} = \frac{7}{6}
  • 45÷32=4×25×3=815\frac{4}{5} \div \frac{3}{2} = \frac{4 \times 2}{5 \times 3} = \frac{8}{15}
  • 910÷65=9×510×6=4560=34\frac{9}{10} \div \frac{6}{5} = \frac{9 \times 5}{10 \times 6} = \frac{45}{60} = \frac{3}{4}
  • 12÷3=12×13=16\frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}
  • 12÷0.5=12×21=1\frac{1}{2} \div 0.5 = \frac{1}{2} \times \frac{2}{1} = 1

Conclusion

In conclusion, dividing fractions is a simple yet powerful operation in mathematics. By following the rule for dividing fractions and simplifying the result, you can solve complex problems and find the quotient of two fractions. We hope this Q&A article has helped you to reinforce your understanding of dividing fractions and has provided you with the confidence to tackle more complex problems.